Question: Rewrite as a simplified fraction. ${0.25\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 256.6666...\\ 100x &= 25.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 231}$ ${x = \dfrac{231}{900}} $ ${x = \dfrac{77}{300}} $